3. Three children want to go out side and play in the rain but their mother will not let them unless they can solve a puzzle.

She brings out a box with 2 red hats and 3 white hats and shows the children. She then blindfolds them and places a hat on each of their heads.
She says that she will allow each child in turn to look at the other two hats and try to determine what their own colour is. “But,” she warns, “if any one of you guesses wrong, you are all staying in.”

The 1st child looks but cannot tell what his hat is.
The 2nd child looks and the same thing happens.
The third child imediately says her hat colour correctly without the removal of the blindfold.

How did she know?

4. There is a mute person who wants to buy a toothbrush. By imitating the action of brushing one’s teeth, he successfully expresses himself to the shopkeeper and the purchase is done. Now, if there is a blind man who wishes to buy a pair of sunglasses, how should he express himself?

5. This puzzle is taken from Richard Smullyan’s Forever Undecided – A Puzzle Guide to Gödel.

On a Monday morning, a professor said to his class, “I will give you a surprise examination someday this week. It may be today, tomorrow, Wednesday, Thursday, or Friday at the latest. On the morning of the day of examination, when you come to class, you will not know that this is the day of the examination.”

Well, a logic student reasoned as follows: “Obviously I can’t get the exam on the last day, Friday, because if I haven’t gotten the exam by the end of Thursday’s class, then on Friday morning I’ll know that this is the day, and the exam won’t be a surprise. This rules our Friday, so I now know that Thursday is the last possible day. And, if I don’t get the exam by the end of Wednesday, then I’ll know on Thursday morning that this must be the day (because I have already ruled out Friday), hence it won’t be a surprise. So Thursday is also ruled out.”

The student then ruled out Wednesday by the same argument, then Tuesday, and finally Monday, the day on which the professor was speaking. He concluded: “Therefore I can’t get the exam at all; the professor cannot possibly fulfill his statement.” Just then, the professor said: “Now I will give you the exam.” The student was most surprised!

What was wrong with the student’s reasoning? (There are some very interesting philosophical issues at play regarding epistemology.)

6. Two fathers and two sons go fishing, they each catch a fish. When they get home, there are only three fish. How can that be if nothing happened to the fish on the way home, or at the lake?

7. How did this man die? A man is dead in a cabin in the middle of the woods in a remote area quite far from any town or city. He was not murdered, did not commit suicide, and did not die of an illness.
How did he die?